Bayesian Multilevel Models and Medical Applications

Deciding which predictor effects may vary across subjects is a difficult issue. Standard model selection criteria are often inappropriate for comparing models with different numbers of random effects due to constraints on the parameter space of the variance components. We propose a straightforward approach for testing random effects in the linear mixed model using Bayes factors. We scale the random effects to the residual variance and introduce parameters that control the relative contributions of the random effects. The resulting integrals needed to calculate the Bayes factor are low-dimensional integrals lacking variance components and can be efficiently approximated with Laplace's method. Our method incorporates default priors and can test multiple random effects simultaneously. We illustrate our method on data from a clinical trial of patients with bipolar disorder and on data from an environmental study of water disinfection by-products and male reproductive outcomes. We extend our method for testing random coefficients to multilevel linear models. A major contribution of our method is the ability to test several variance components from multiple factors simultaneously, and to do so for nested, non-nested, or cross-nested multilevel designs. We illustrate our method on a study investigating significant predictors of infant birth weights in New York City. Random effects are often used for jointly modeling distributions of correlated longitudinal and survival outcomes. These methods generally require strong parametric assumptions and can be difficult to implement. We propose a straightforward approach to evaluate the effect of a treatment or baseline predictor on both longitudinal and survival outcomes simultaneously. We define cutpoints of interest in the longitudinal outcome and time-to-event endpoints based on time to reach a given cutpoint or the survival event, whichever comes first. We use multivariate time-to-event methods on the resulting endpoints to evaluate the effect of the treatment or baseline predictor. The method is particularly attractive in clinical trial settings in which the primary analysis must be specified a priori. We illustrate the method on data from a study of chronic lung disease